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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
We establish the status of the Weyl double copy relation for radiative
solutions of the vacuum Einstein equations. We show that all type N vacuum
solutions, which describe the radiation region of isolated gravitational
systems with appropriate fall-off for the matter fields, admit a degenerate
Maxwell field that squares to give the Weyl tensor. The converse statement also
holds, i.e. if there exists a degenerate Maxwell field on a curved background,
then the background is type N. This relation defines a scalar that satisfies
the wave equation on the background. We show that for non-twisting radiative
solutions, the Maxwell field and the scalar also satisfy the Maxwell equation
and the wave equation on Minkowski spacetime. Hence, non-twisting solutions
have a straightforward double copy interpretation.
